Design of an All-Purpose Terrace Farming Robot

When designing a scissor-lift mechanism, the location of the linear actuator’s attachment is critical because it directly impacts the potency of the system, that is, the mechanical advantage and the velocity ratio, and thereby influencing the choice of the linear actuator to actuate the system, and hence, the overall cost. In short, the position variables of the linear actuator attachment affect the force output and the stroke length of the actuator. There are other design parameters such as the link lengths, link thickness, number of scissors, etc. that directly influence the force output and the stroke length of the actuator.

Before picking an ideal set of position variables, it is necessary to establish equations for force output and the stroke length of a linear actuator in terms of the scissor-lift position variables. Without loss of generalisation, we can consider a $n$ stage scissor lift mechanism as shown in Fig. 4. The linear actuator has one end static and the other translating. The translating end is attached to a point on a positively sloping link in the scissors and the static end is attached to a fixed support. When the translating end of the actuator extends, it will cause the scissor-lift to extend and vice versa.

As shown in Fig. 4, A is the point where the translating end of the linear actuator is attached to the scissor and hence, it is the point where force is applied. B is the point where the static end of the linear actuator is attached. O is the origin and XY is the reference co-ordinate axes for the analysis. Various symbols used and their corresponding descriptions are tabulated in Table 1.

Here, $a$, $b$, $\theta$ and $n$ are the only independent variables. $D$ and $i$ are assumed to be constant in our analysis. $i$ is set equal to $n-1$. The expressions $h$, $l$ and $F$, derived in scissor-lift , in terms of the independent variables, are shown in (1), (2), and (3), respectively. The stroke length of the linear actuator can be obtained by subtracting the length of the actuator in the maximum extended state and the maximum compressed state as expressed in (5). It is also required to find out the maximum force required to actuate the scissor-lift to choose the linear actuator. The force required to actuate the scissor-lift will be maximum when the scissors are in the most compressed state, i.e., when $\theta=\theta_{min}$. The maximum force, $F_{max}$, can be expressed as in (4). The variation of $F_{max}$ and $S$ with respect to $a$, $b$, and $n$ is clearly illustrated in Fig. 5(a) and Fig. 5(b), respectively. With an increase in both $a$ and $b$, $F_{max}$ decreases and $S$ increases. Also, with a increase in $n$, $F_{max}$ increases and $S$ decreases.

Where $\lambda=\left(\overline{a}^{2}-(i+a)^{2}\right)$ and $\overline{a}=1-a$. Clearly, $F_{max}$ and $S$ are conflicting functions with respect to $a$ and $b$. Hence, we formulate this problem as a multi-objective optimization problem, where the conflicting objectives, $F_{max}$ and $S$, are to minimized. The problem is mathematically formulated as shown in (6).

Here, $D_{min}$ is the minimum link length required to climb the step of height, $H$, calculated as shown in (7).

Since a single solution cannot optimise all the conflicting objectives simultaneously, we seek to optimise the objective functions and present the Pareto Front. The Decision Maker, then, can choose a linear actuator from the Pareto Front solution set based on the use case of the robot.

Multi-objective evolutionary algorithms (MOEAs) have grown in popularity in recent years as a result of their ability to find many Pareto-optimal solutions in a single simulation run. Algorithms such as Non-Dominated Sorting Genetic Algorithms (NSGA-II) 996017 , Multi-Objective Grey Wolf Optimizer (MOGWO) mirjalili2016multi , Multi-Objective Particle Swarm Optimizer (MOPSO) reyes2006multi , Multi-Objective Bonobo Optimizer (MOBO) das2020multi are widely used to obtain Pareto-front in real-world multi-objective problems.

Here, we are employing gamultiobj, a MATLAB package that uses a controlled, elitist genetic algorithm, to solve the constrained multi-objective optimisation problem (6). We set the population size to be $200$ and the Pareto fraction as $0.7$. We designed a robot for climbing stairs of height up to $40$ cm. In our case, choosing $n>4$ seemed sub-optimal and hence, we added an additional constraint on the number of scissors, $n=\{2,3,4\}$. The load $L$ moved by the scissor-lift and the height $H$ of the stair is fixed as 250 N and 40 cm, respectively. Solving the optimisation problem separately for each value of $n$, three different Pareto optimal fronts were obtained as shown in Fig. 6.

We have added additional constraints on the maximum force ($F_{max}\leq 1000$ N) and stroke length ($S\leq H$) to filter out the non-feasible values. The filtered values of $F_{max}$ and $S$ along with the corresponding independent variables have been tabulated: (LINK). The Decision Maker can use the table as a datasheet to compare them to other linear actuators on the market and select one based on price and availability. In our case, we chose a linear actuator with $25$ cm stroke length and $1000$ N maximum load. This choice of linear actuator introduced a factor of safety of approximately $1.74$ in the design. The final scissor-lift design parameters along with the linear actuator specifications chosen for the robot prototype are tabulated in Table 2.

Further, the thickness of the scissor links needs to be optimised between maximum stress, deformation due to bending and buckling. Also, while optimising the thickness, the space for the placement of the linear actuators between the scissors has to be maximised. Given the problem, a simplified model of the scissor lift mechanism with two crosses used in the prototype was imported to ANSYS 17.1 for structural simulation analysis as shown in fig. 7. This model refers to the maximum extended position of the scissor lift mechanism. In the simulation, considering 40 kg as the weight of the robot, respective forces and torques were applied to the ANSYS model at the ends marked as 1,2,5 and 6 in fig. 7. The joints indicated as 3 and 4 in fig. 7 are fixed during the simulation. Two commonly used materials – Steel and Aluminium, each with four commercially available and relevant thicknesses – 2 mm, 3 mm, 5 mm and 7 mm – were selected for the simulation study.

The factor of safety due to the maximum stress ($N_{S}$), and the absolute maximum total deformation ($\delta_{max}$) and its components in X - ($\delta_{max}|_{X}$) and Y-direction ($\delta_{max}|_{Y}$) were analysed during the ANSYS simulation study. Figure 8 shows the values of parameters analysed during the study. It is to be noted that $\delta_{max}|_{X}$ physically signifies the deformation due to bending and buckling of the scissor links. It was found that the safety factors ($N_{S}$) for all the four thicknesses considered were similar for both metals. However, aluminium showed a higher maximum deformation than steel with the same thickness both in X- and Y-direction. Selecting a thicker aluminium link would lead to reduced space for the linear actuator. Even so, choosing steel would mean a heavier mechanism. Hence, optimising all the requirements for the prototype developed by us, steel links of 3 mm thickness were used to provide sufficient strength, lower maximum deformation and more space for accommodating the linear actuator.

The above-mentioned procedure shall be followed to choose various design parameters of the scissor lift mechanism optimally, depending on the size, weight and use case of the robot.

The disc plough attached to the robot performs secondary tillage that helps in seedbed preparations and intercultural operations. It creates refined soil conditions following primary tillage and provides breaking of clods and mixing of crop residues smith1976farm . Disc plough is chosen because it is long-lasting, has more mixing action than inversion, and works well in sticky soil conditions CHANDRAMOULI201823702 . Smooth edged discs have been used as they have low maintenance costs and work well even if substantial parts of the disc are worn out in abrasive soil.

The disc angle is defined as the angle at which the plane of cutting edge of the disc is inclined to the direction of travel, as shown in Fig. 11(b). The tilt angle is defined as the angle at which the plane of cutting edge of the disc is inclined to vertical, as illustrated in Fig. 11(c). In kepner1990principle , it was found out that these angles influence the depth and width of cut of the soil. It was concluded in osman2011effects and bukhari1992effect that, with an increase in disc and tilt angles, the field capacity and the power required to plough the field increased. Hence, it becomes important to choose suitable values for these angles while designing the mechanism. From article_el_naim , the optimum values of disc and tilt angles are found to be between $42^{\circ}$ to $45^{\circ}$ and $15^{\circ}$ to $20^{\circ}$.

In Aarohi, six circular smooth edge discs attached to a shaft have been used. They are oriented with disc angle and tilt angle as $45^{\circ}$ and $15^{\circ}$, respectively, in order to reduce the radial force. Alternative discs are oriented in opposite directions to eliminate side thrust force on the robot. This novelty in design has allowed removing the additional rear furrow wheel which is used in the reduction of side thrust in conventional mechanisms. The shaft that connects the discs is powered by a motor to control the rotational speed of the discs. The shaft is rotated such that the friction acts on the discs in the direction that supports the motion of the robot reducing the load on the motors that power the wheels.

It is placed immediately after the disc plough with sufficient clearance. The primary roller levels the ploughed soil, thereby flattening the soil. Torsional springs are mounted at the ends of the roller to give compliance and reduce additional loads on the wheels of the robot and ensure proper levelling of the soil.

V-shaped furrowers are used to make grooves of appropriate depth on the flattened land. In the robot, four V-shaped metal plates are connected to the PSR mechanism’s base plate through a bracket. Although the V-shaped metal plates are not the most optimal design for furrowers smith1976farm , they have been considered due to their relative simplicity in manufacturing and assembly. The linear actuator connected to the base plate provides the downward force required for furrowing.

Sowing seeds precisely is the next and a very crucial step in precision agriculture. Recently, a lot of researchers have been focussing on precision seeding techniques as a driving direction for modern agriculture technology singh2005optimisation ; yasir2012design . It can save a lot of seeds and effectively control the inter-seed distance as well. Broadly, two kinds of seed metering devices for grains have been proposed in literature based on the mode of operation: (a) Mechanical seeder, and (b) Pneumatic seeder. While pneumatic seed metering devices have proven to have better performance in terms of a more uniform distribution and quality of feed index, several researchers have advocated the use of mechanical seeding for its low cost and reliability especially for the sowing of crops like wheat minfeng2018optimal ; yu2021design . In conventional mechanical feeders, a ground wheel is typically used to drive the seed metering device article_ground_wheel . However, occasional wheel slips and resistance in an uneven terrain results in poor performance of this system in controlling the seed rate. Zhai et al. jianbo2014design improved upon this system by designing a control system that could keep the rotational speed of the seed-metering device consistent with the seeder’s working speed and achieved good performance. Jin et al. minfeng2018optimal also solved the problem of poor consistency management by adjusting the opening of fluted rollers by a novel mechanism. Our seeder system is a low-cost yet efficient solution to the automated seeding process and drives inspiration from these designs.

As shown in Fig. 12, the seed metering module in Aarohi consists of four boxes from where a seed feeder wheel puts the seeds in the funnel, which is then connected to a gravity drop seed tube. The other end of the tube is placed just behind the V-shaped metal plates of the liner, to ensure the falling of seeds inside the furrow. The seeder boxes are slotted and attached to the chassis. The seed feeder wheels are connected to a shaft which is in turn connected to a stepper motor. This stepper motor is attached to the chassis through L-brackets and it is responsible for the prevention of interlocking among the seed granules and also controlling the longitudinal inter-seed distance during sowing operation.

A secondary roller is used to fill the furrows and level the ground. This rolling operation creates a smooth and firm seedbed, presses the seeds into the soil thereby eliminating air pockets, and helps in retaining the soil moisture for a longer period, thereby allowing for faster germination smith1976farm .

The estimation of the pose and orientation of the robot is done using ground odometry data from wheel encoders and inertial measurements from IMU. As ground odometry tends to be inaccurate in the presence of wheel slipping, it is often fused with other forms of inputs like lidars and GPS for accurate localisation. We use an Extended Kalman Filter (EKF) method to fuse different localisation estimates. While GPS sensors provide global position data, they were not found to be of much use in the robot due to large errors (1̃m). The EKF method effectively weights the different estimates with the uncertainty associated with them and outputs the robot position. Based on these low-level inputs, the overall localisation module as shown in Fig. 14, outputs high-level location information that includes the step number (from the top), crop row number and distance from sides of the terrace.

We use the width estimation lidars $W_{l}$ and $W_{r}$ to estimate the minimum terrace width at the current step. These lidars are pointed downwards at an angle of $45^{\circ}$ from the horizontal. For the purpose of describing the method for terrace width estimation, assume that the robot is moving such that the terrace wall is towards its left, as shown in Fig. 16. A new width measurement is taken when there is a sudden change in the readings of lidars $W_{l}$ and $W_{r}$. Using simple geometry, the terrace step width can be estimated as

Where $\phi$ is the angle between robot heading and the terrace wall, given by

Here $d_{W}$ and $d_{L}$ are the robot width and lengths, as illustrated in Fig. 15. This width estimation system allows for the robot to handle terrace steps with variable widths along the length, and allows the planning module to account for the variations accordingly. Since the system depends on sudden changes in the width estimation lidar readings, it can estimate width only when the nearest distance between robot midline and the terrace step end crosses the value $L_{db}\tan 45^{\circ}$.

To measure the distance from the robot’s body-fixed frame and the terrace edge, an image processing based edge detection algorithm is deployed. It uses a modified urban road stop-line detection algorithm as proposed in seo2014vision . A vertical gradient filter is applied on the input image which highlights horizontal features. Next, the probabilistic hough transform is applied on sufficiently large clusters with a horizontal spread to detect horizontal lines, and relatively close horizontal lines are merged into super-clusters, and the bottom-most super-cluster is detected as the terrace edge, as shown in Fig. 17.

Inverse homography and static frame transforms are used to convert the distance pixels to meters and calculate the distance between the terrace edge and the robot’s body-fixed frame. We test and validate the algorithm multiple times on even and uneven edges to ensure robust detection.

The fail-safe system for fall avoidance comprises of four 1D lidars mounted at all the edge centres of the robot, looking downwards making an angle $25^{\circ}$ with the horizontal Fig. 16. These lidars form a safe zone around the robot, and if a sudden increase in values of any of these lidars is detected, an emergency stop is triggered and all autonomous operations are stopped. The safe zone is an imaginary rectangle with its edges located at an inner distance $L_{db}\tan 45^{\circ}$ from the robot edges, which, when the linear actuators are fully contracted, is about 12 centimetres. This system stops the robot from falling off terrace edges, which might happen due to planning errors or system uncertainties.

Based on the number of rows of crops present in the terrace, the planner generates the primary path that the robot has to traverse on the terrace. Within the current method, the primary path is a straight line along the terrain at a constant distance from the wall of the terrace. The planner takes as input the number of rows of crops to devise an optimal path that traverses through each plant row while minimising time and actuation cost. As exemplified in Fig. 18, if $n_{\rm croprow}=3$, the path generated ensures that the robot returns in the same orientation as it entered in order to save actuation costs of zero degrees turn. The planner also takes into account the spatial constraints of the robot and the terrace width estimate to maintain safe margins from both sides of the terrace. The planner prevents the robot from entering into any unsafe zones along the terrace.

The software stack provides the provision for the farmers to input a desired agricultural strategy which acts as an input to the planner. Before starting the work on terrain, the planner sends a query to the agriculture strategy module as shown in Fig. 14. Based on the user inputs provided, the planner module accordingly plans the traversal path as well as the activation required for different farming tools to perform agricultural activities. Hence a flexible strategy can be maintained from terrain to terrain and crop to crop. Different combinations of farming activities can be fed into the strategy module in order to achieve different goals under varying circumstances.

Due to the difference in the mechanical response of both scissor lift mechanisms, the pitch of the chassis while lifting up may not be zero when both the actuators are given the same input causing instability. We use a PID controller for maintaining zero pitch that ensures the robot remains stable at all times. We estimate the error in pitch and provide corrective feedback to the linear actuators to keep the pitch zero at all times.

Here $A_{f}$ and $A_{b}$ actuator inputs for the front and back linear actuators. $\theta$ denotes the pitch of the robot, as shown in Fig. 20. This method allows us to achieve two different objectives while controlling the pitch of the robot,

1. 1.

   Difference in input is controlled based on the pitch of the chassis.

2. 2.

   Average actuation input is controlled based on the change in velocity of the base to ensure a constant velocity of ascent/descent.

We observe that a standard PID performs well during normal operation but the controller performance depletes on addition of a payload and in presence of external forces. As observed in Fig. 21, a standard PID in presence of an external weight leads to a change in the asymptotic value of the pitch which can cause instability. In order to address this we use an adaptive PID algorithm based on (Alonso2013SelftuningPC, ). The algorithm uses a modified version of the MIT rule for altering PID gains given as,

where $\gamma_{p},\gamma_{I},\gamma_{D}$ are tunable parameters and $e(t),\dot{e}$ are standard error and error rate measurements whereas $e_{m}(t),\dot{e}_{m}(t)$ are filtered values through a low pass filter. This algorithm helps to handle noises in the system effectively while preventing extremely high values for the PID gains.

As shown in Fig.22. We observe improved performance with adaptive PID in comparison to standard PID controller in maintaining zero pitch with external disturbances.

Given an optimal path from the planning module, we need to ensure accurate tracking of the path considering external forces and environment uncertainties. We use a modified pure-pursuit based controller for this purpose which takes into consideration the kinematic constraints of the robot and external disturbances due to uneven terrains. Pure pursuit is a goal-oriented approach where the wheel velocities are calculated to drive the robot along a circular path from the current position to a final goal position on the optimal path which is at a particular look-ahead distance from the robot. As shown in Fig. 23, the robot considers the point on the path at a distance of $l_{d}$ as the goal. For smooth trajectories, the robot is treated as an ackermann vehicle, and based on Ackermann geometry, $\delta$ is the steering angle, $v_{x}$ is the longitudinal velocity and $R$ is the turning radius. $\alpha$ is the central angle for the turn and its value is calculated from the differential value of the distance measured by the pair of lidars facing the adjacent wall. The look-ahead distance is the parameter that needs to be tuned. We use an adaptive look-ahead distance proportional to the velocity of the robot to ensure smooth control inputs. Hence, we obtain the required steering angle using

Using the steering angle, we can calculate the angular velocity using

Once we have the required velocity $v$ and angular velocity $\omega$, we can estimate the left and right wheel velocities using

The standard pure pursuit algorithm only considers kinematic constraints and ignores dynamic forces on the tires and external disturbances which might cause instability especially in uneven terrains like agricultural fields. In order to address this issue we implement an adaptive Pure Pursuit algorithm similar to (Hoffmann2007AutonomousAT, ) accounting for ground reactions causing side slips. An added gain term is added to the nominal input which acts as an active damper against the ground reaction forces causing slip. The modified steering control input is calculated as,

where $r_{ref}$ is the rate of change of yaw for the reference trajectory and $r$ is the change of yaw for the robot. The added gain of $k_{d,yaw}$ requires to be tuned based on the range of operating velocity of the robot.

The controller shows good performance in terrace farming tasks and converges to zero cross track error even in rough terrains. The Fig.24 shows the convergence data of the controller implemented in a real-world testing environment.